Personally, I really think the only thing that truly matters is whether or not the CPR card that you have meets AHA requirements. The Red Cross Professional Rescuer version I believe matches AHA. I generally prefer to do the AHA CPR class because more providers recognize that as evidence of the appropriate level of training. The American Red Cross does provide that level of training, however, they also provide several other levels of CPR training. Therefore it is possibly more confusing to do American Red Cross certification than the American Heart Association CPR certification.
A few years ago I took a CPR class that included the AED. The class was a professional level rescuer class. I had to do more explaining about that class than I would have had to do if I had taken the American Heart Association class of the same level. I think mostly it was because the course included AED but was not specifically listed on the card.
If in doubt, ask them what they require.